The problems you're discussing are very common across RPG groups. We can break the issues down between 'combat' (hold person) and 'non-combat' (suggestion) encounters.
How Do I Make Combat Encounters More Challenging (without increasing the number of monsters)
Use more powerful monsters
This one should be relatively obvious, as the higher the CR of the monster, the more difficult (in theory) it is to defeat. If you find that your party is steamrolling your 4 CR6 monsters, start looking at having fewer, higher-level monsters. As the CR increases, the lethality and number of abilities the monsters have quickly increase. A CR8 monster can do things that a CR6 can only dream of, and that can give your party a lot to mull over when they're fighting one.
Adapt the monsters to your party's power level
Your Divination Wizard is using hold person every chance they get? Well, the BigBad realized this and sent his non-humanoid lieutenants after the party (hold person only works on humanoid creatures). Your Sorcerer is dropping fireballs like its their job? The now-terrified king of the region sent some fire-elementals to ruin their plans. Your Barbarian is crushing everything within its reach with a hammer? A few flameskulls should give them something to think about.
Customize the monsters you were going to use anyways
The evil wizard invented a tattoo that, when applied to humanoid characters in the proper fashion, gives them advantage on Wisdom saving throws (and makes it much more difficult to Hold Person or Suggest them). The Orc warchief becomes enraged when burned. The ultra-strong giant that defends the entrance to the cave has been imbued with a special power that gives him legendary resistance.
More encounters per day
This is probably the biggest one. The DMG will recommend you put your party through 8 encounters per long rest. However, most normal people do 2-3 encounters per day, which makes spellcasters extremely powerful. Your Divination Wizard gets 2 portent dice a day. If he has to balance that between 8 combat encounters and 6 social encounters, then there will be many times when there just aren't any portent dice left to ruin your encounter. However, if there are only a few encounters per day, then your Wizard will likely be able to use portent whenever they need to, which is going to derail your plans.
How Do I Make Non-Combat Encounters More Challenging
Have your NPCs start adapting to the players
By the second or third time the BigBad's plans are derailed because of a well-placed Suggestion spell, they should start putting contingency plans into action. Sure, they may not be able to work out that it was specifically Suggestion that was being cast, but eventually they're going to realize that someone is able to force previously-loyal minions to perform actions. A smart enemy would start sowing misinformation, creating tests (tell each of your top 10 minions that the Sword of PCDesire is hidden in a different location. Whichever location the PCs raid corresponds to the minion they were able to charm), and generally making Suggestion less powerful.
This is a divisive issue, but when low-level PCs get access to spells as powerful as Suggestion, sometimes you just have to fudge it. The king of the land rolled a nat 1 on their save? Maybe it was actually a 15, so they passed. The group manages to cast Suggestion on the one NPC that knows the location of the BigBad's lair? Well, maybe he only thought he knew. Maybe he didn't actually know at all, it was the guy standing next to him who knew, and you just mixed up your notes. Maybe the BigBad had been planning to move for months, and just never got around to telling this guy about the changes.
I want you to ask yourself two questions before you start doing any of this.
- Am I prepared for this to get worse as time goes on?
High-level PCs are a force to be reckoned with. 8 high-level PCs are going to cause you some major pain. There is always going to be something that they uncannily excel at, and short of re-writing reality you're probably going to have to deal with it. To make matters worse, they're naturally going to gravitate to the things they do well and shy away from the things they do poorly. You haven't stated their min-max attitude, but if they metagame their characters at level-up time and before/after combat, it'll be near impossible to devise consistently challenging encounters that don't simultaneously run the risk of one-shotting someone, or having an unlucky roll turn into a TPK. In that case, you'll likely be forced to simply increase the number of encounters per day, and then taper the encounters off once the party starts getting worn out.
- Do my players see a problem with the current setup?
I played with a group that absolutely loved to crush combat encounters. The more challenging the encounter, the less fun they had. They didn't care how easy it was, or how short rounds were. They just wanted to win, and win hard. That's not to say that your group is thinking that way, but are you sure that the players want it to be more challenging? If they do then go right ahead, but before you go through all this work, make sure the players will actually appreciate it.